Stochastic fractional partial differential equations driven by Poisson white noise
Annales mathématiques Blaise Pascal, Volume 15 (2008) no. 1, pp. 43-55.

We study a stochastic fractional partial differential equations of order α>1 driven by a compensated Poisson measure. We prove existence and uniqueness of the solution and we study the regularity of its trajectories.

On étudie une équation aux dérivées partielles stochastiques fractionnaires d’ordre α>1 dirigée par une mesure de Poisson compensée. On montre l’existence et l’unicité de la solution et on étudie la régularité de ses trajectoires.

DOI: 10.5802/ambp.238
Classification: 26A33,  60H15
Keywords: Stochastic partial differential equations; fractional derivative operator; Poisson measure.
Salah Hajji 1

1 Department of Mathematics Faculty of Sciences Semlalia Cadi Ayyad University BP. 2390 Marrakesh, MOROCCO.
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Salah Hajji. Stochastic fractional partial differential equations driven by Poisson white noise. Annales mathématiques Blaise Pascal, Volume 15 (2008) no. 1, pp. 43-55. doi : 10.5802/ambp.238. https://ambp.centre-mersenne.org/articles/10.5802/ambp.238/

[1] S. Albeverio; J.-L. Wu; T.-S. Zhang Parabolic SPDEs driven by Poisson White Noise, Stochastic Processes and Their Applications, Volume 74 (1998), pp. 21-36 | DOI | MR | Zbl

[2] E. Saint Loubert Bié Etude d’une EDPS conduite par un bruit Poissonnien, Probability Theory and related fields, Volume 111 (1998), pp. 287-321 | DOI | Zbl

[3] R. Dalang; C. Mueller Some non-linear s.p.d.e.’s that are second order in time, Electron. J. Probab., Volume 8 (2003), pp. 1-21 | Zbl

[4] L. Debbi On some properties of a High Order fractional differential operator which is not in general selfadjoint, Applied Mathematical Sciences, Volume 1,27 (2007), pp. 1325-1339 | MR

[5] L. Debbi; M. Dozzi On the solutions of nonlinear stochastic fractional partial differential equations in one spatial dimension, Stoc. Proc. Appl., Volume 115 (2005), pp. 1764-1781 | DOI | MR | Zbl

[6] N. Fournier Malliavin calculus for parabolic SPDEs with jumps, Stochastic Processes and Their Applications, Volume 87 (2000), pp. 115-147 | DOI | MR | Zbl

[7] N. Ikeda; S. Watanabe Stochastic differential equations and diffusion processes, North-Holland Publishing Company. Mathematical Library 24., Holland, 1989 | MR | Zbl

[8] I. Podlubny Fractional Differential equations: an Introduction to Fractional Derivatives, Fractional Differential equations, to Methods of Their Solution and Some of their Applications, Academic Press, San Diego, CA., 1999 | MR | Zbl

[9] J.B. Walsh. An Introduction to stochastic partial differential equations, Lecture Notes in Mathematics 1180, Springer Berlin / Heidelberg, 1986, pp. 266-437 | MR | Zbl

[10] J. Zabczyk. Symmetric solutions of semilinear stochastic equations, Lecture Notes in Mathematics 1390, Springer Berlin / Heidelberg, 1988, pp. 237-256 | MR | Zbl

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